please show the steps especially when you use arctan.
the answer is suppose to be 10(1/5*tan^-1*x/5)
the answer is suppose to be 10(1/5*tan^-1*x/5)
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∫dx/(x² + 25) = 1/25*∫dx/(x²/25 + 1)
u = x/5
5 du = dx
1/5*∫du/(u² + 1) = 1/5*arctan(u) + C
= 1/5*arctan(x/5) + C
u = x/5
5 du = dx
1/5*∫du/(u² + 1) = 1/5*arctan(u) + C
= 1/5*arctan(x/5) + C